MATH 111 – Week 4 – Trigonometric Formulas and Equations

MATH 111 – Week 5 – Trigonometric Formulas and Equations

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1. Which solution describes every angle that has a $\frac{π}{3}$ reference angle in the first quadrant? (Note that n is an integer.)

• $\frac{π}{3}$
• $\frac{π}{6}$ + n
• $\frac{π}{3}$ + n
• $\frac{π}{3}$ + πn
• $\frac{π}{3}$ + 2πn

2. Which solution describes every angle that has a 25˚ reference angle in the second or fourth quadrant?

• 25˚
• 25˚ + n
• 155˚ + 90n
• 155˚ + 180n
• 155˚ + 360n

3. Solve for x in 2sinx = 1.

• 60˚
• 30˚
• -30˚
• -60˚
• There is no answer.

4. Solve for x in 2sinx = 1 when x is between 0˚ and -180˚.

• 60˚
• 30˚
• -30˚
• -60˚
• There is no answer.

5. Solve for x in 2sinx = -1.

• 60˚
• 30˚
• -30˚
• -60˚
• There is no answer.

6. Solve for x in 2sinx = -1 when x is between -90˚ and -180˚.

• -30˚
• -60˚
• -120˚
• -150˚
• There is no answer.

7. Solve for x in 2sinx = -1 when x is between 90˚ and 270˚.

• 30˚
• 60˚
• 210˚
• 240˚
• 330˚

8. Which answer is a solution to the equation 2cosx = 0?

• $\frac{π}{2}$
• $\frac{π}{3}$
• $\frac{π}{4}$
• $\frac{π}{6}$
• π

9. Solve for x in 3cosx = 0 when x is between π and 2π.

• π
• 2π
• $\frac{π}{2}$
• $\frac{2π}{3}$
• $\frac{3π}{2}$

10. Solve for x in sin$^{2}$x = sinx.

• x = 0
• x = $\frac{π}{4}$
• x = $\frac{π}{2}$
• x = 0, x = $\frac{π}{2}$
• x = $\frac{π}{2}$, x = $\frac{π}{4}$

11. Solve for x in sin$^{2}$x = -sinx.

• x = 0
• x = $\frac{π}{2}$
• x = $-\frac{π}{2}$
• x = 0, x = $\frac{π}{2}$
• x = 0, x = $-\frac{π}{2}$

12. Solve for x in sin$^{2}$x = -sinx when $\frac{π}{2}$ ≤ x ≤ $\frac{3π}{2}$.

• x = $\frac{π}{2}$
• x = $\frac{-π}{2}$
• x = $\frac{3π}{2}$
• x = π, x = $\frac{3π}{2}$
• x = $\frac{π}{2}$, x = $-\frac{π}{2}$

13. Solve for x in sin$^{2}$x = sinx when 0 ≤ x ≤ -π.

• x = 0
• x = $-\frac{π}{2}$
• x = -π
• x = 0, x = -π
• x = 0, x = $-\frac{π}{2}$

14. Solve for x in 2sin$^{2}$x $-$ 1 = sin$^{2}$x.

• x = 0˚
• x = 60˚
• x = 120˚
• x = 0˚, x = 30˚
• x = -90˚, x = 90˚

15. Solve for x in sin$^{2}$x $-$ 2 = -sinx when x is between 0˚ and 180˚

• x = 30˚
• x = 90˚
• x = 150˚
• x = 0˚, x = 120˚
• x = -30˚, x = 60˚

16. Solve for x in 4sin$^{2}$x + 3sinx + 2 = -3sinx.

• x = 0
• x = $-\frac{π}{3}$
• x = $\frac{5π}{6}$
• x = $\frac{2π}{3}$, x = π
• x = $-\frac{π}{6}$, x = $-\frac{π}{2}$

17. Solve for x in 4sin$^{2}$x + 3sinx + 2 = -3sinx when 90˚ ≤ x ≤ 270˚.

• x = 90˚
• x = 150˚
• x = 270˚
• x = 0˚, x = 90˚
• x = 210˚, x = 270˚

18. Simplify sin(165˚).

• -0.64
• -0.26
• 0
• 0.26
• 0.64

19. If sin$\bigl(\frac{π}{16}\bigr)$ = 0.1951 and cos$\bigl(\frac{π}{16}\bigr)$ = 0.9808, what is cos$\bigl(\frac{π}{8}\bigr)$?

• 0.92
• 0.48
• 0.12
• -0.48
• -0.92

20. Simplify the expression tan$^{2}$(x) + tan$^{2}$(x) cos(2x) using the reduction formula for tangent.

• 2sinx
• 1 + cos2x
• 1 + tan2x
• 1 $-$ cos2x
• 1 $-$ sin2x

21. Using the half-angle formula, what is sin$\bigl(-\frac{π}{12}\bigl)$?

• -0.64
• -0.26
• 0
• 0.26
• 0.64

22. What is cos(3x) cos(4x)?

• cos(12x)
• sin(3x) + cos(4x)
• $\frac{1}{2}$[cos(-x) + cos(7x)]
• $\frac{1}{2}$[cos(-x) $-$ cos(7x)]
• $\frac{1}{4}$[sin(-5x) $-$ cos(12x)]

23. What is sin(6x) $-$ sin(4x)?

• -$\frac{1}{2}$sin(2x)sin(4x)
• -2cos(4x)sin(x)
• $\frac{1}{2}$cos(4x)sin(x)
• 2sin(2x)cos(4x)
• 2sin(x)cos(5x)